One of the most formidable exemplars of the Cult of the Bad is Florence Foster Jenkins, a wealthy woman who publicly sang the most challenging coloratura arias, despite having zero breath control and a tendency to hit about one out of every ten notes correctly. Recordings suggest the dying cries of a small mammal. In December 1944, she rented (and filled) Carnegie Hall — an event that is the climax of Stephen Frear’s Florence Foster Jenkins, starring Meryl Streep as the aging chanteuse and Hugh Grant as her protective common-law (second) husband, St. Clair Bayfield. It’s a wobbly, uneven, ultimately wonderful film — its unevenness befitting its title character, who we come to love despite her loopy lack of awareness of her own deficiencies.

Her life, it turns out, is a better exemplar of the ability to use illusion (and, it must be admitted, the power of money) to keep tragedy at bay. The “worst singer of all time” was actually a childhood piano prodigy who performed to acclaim. But a falling-out with her wealthy father led to an elopement with a ne’er-do-well, who promptly gave her syphilis. (This was the 19th century, long before penicillin.) The infection ruined her hands and possibly affected her sense of pitch (although the film doesn’t spell that out), but she ended up inheriting her family fortune and set about becoming a patron of the New York classical-music scene. In that role, she was exceedingly generous, and, apart from her compulsion to perform, rather selfless.

Florence Foster Jenkins (written by Nicholas Martin) opens with a cringeworthy evening at the Verdi Society (which she founded), a recital that builds to a series of tableaux vivants — one of which shows the plump Florence lowered from the flies as a goddess-muse for Stephen Foster, as he struggles to write “Oh! Susanna.” She does not, however, sing. In her opulent apartment, she entertains floridly obsequious directors of various music organizations (who want money), as well Maestro Arturo Toscanini himself (who also wants money). The sound of Florence Foster Jenkins in song comes nearly half an hour into the movie, cunningly withheld in the manner of the shark in Jaws. We experience this through the eyes of her new, uppity young pianist, Cosme McMoon (Simon Helberg), who auditioned for the job with the impression that it would make his name in the New York music scene. His expression on first hearing — in the company of an effusive vocal coach and her reassuring husband — recalls what you’d see on Candid Camera. But it’s no joke.

At times, especially early, Florence Foster Jenkins comes dangerously near to camp. Frears has a tendency to use artificial lenses — wide-angle, fishbowl — and some of the supporting performances are a mite over the top. As a stereotypical floozy, the often-great Nina Arianda would fit into a summer-stock production of Annie, and even Helberg (who grows in the role and is finally terrific) does too much mugging with the camera too close.

Hugh Grant grounds the movie. Bayfield is the true protagonist, and few have ever had to navigate such emotionally precarious waters. His devotion to Florence is palpable — but he’s clearly a “kept” man, with the slight seediness that the phrase implies. Owing to her syphilis, he and his wife have never had carnal relations; he has a separate apartment and (unbeknownst to Florence) a bohemian girlfriend (Rebecca Ferguson, who triumphed last year in the fifth Mission: Impossible movie). Diligently, Bayfield pays off audience members and even critics for his wife’s small recitals — and refuses to admit Earl Wilson (Christian McKay) of the New York Post, who won’t accept a bribe and wants to write about Florence for real. Once or twice Grant shows his trademark gift for looking abashed in the midst of farce, but that was his youthful persona. This performance is a model of understatement: low-key but rich in feeling. He’s superb.

And La Streep? She has one flaw: She is a decent singer and cannot, no matter how hard she tries, sound as horrible in song as Florence Foster Jenkins really did. But she comes awfully (and I mean awfully) close. Her trills are shrill, her high notes toneless howls. At the end of the day, when Bayfield tucks her into bed and removes her wig (she is bald), Streep looks slack and pathetically undefended; she makes you understand why Florence’s husband remains so close and is always poised to shield her from mockery. In one scene, she listens to a youthful Lily Pons (Aida Garifullina) and tears swim into her eyes. She knows transcendentally great singing. Why can’t she hear herself? Streep makes you watch and wonder.

Earl Wilson is the villain of Florence Foster Jenkins and, as a critic, his cruelty cut me deeply. What can a critic in such circumstances do? Collect that bribe and write what isn’t true, and therefore allow incompetence to flourish? Wilson perceives arrogance and unbridled ego, and perhaps the fruits of privilege — and that’s understandable, given that he’s not, as we are, watching a biopic of Florence Foster Jenkins and being given an inside view of her noble soul. I think it comes down to tone. The audience in Carnegie Hall begins by laughing at this woman, so Wilson’s review assails someone already assailed — much as, today, a critic might write a lengthy and devastating review of Rebecca Black’s “Friday.”

The Cult of the Bad certainly upends one’s sense of critical responsibility. Truly bad artists are now practically sanctified and played by people like Meryl Streep or Martin Landau, who won an Oscar as Bela Lugosi — an award that the real Lugosi never came within miles of. What’s happening is that we’re learning to see beyond the art.

Mark O’Connell’s book Epic Fail: Bad Art, Viral Fame, and the History of the Worst Thing Ever does not dwell on Jenkins, but he is particularly enlightening on the subject of the grisly prose-stylist Amanda McKittrick Ros — who was so ghastly that she inspired essays by the likes of Aldous Huxley, and so arrogant in her assurance of her greatness that she wrote her editor, “What think you of this [Nobel Prize for literature]? Do you think I should make a ‘dart’ for it?” O’Connell writes of Ros:

There’s something paradoxically inspiring about her complete (and completely misplaced) confidence in the magnitude of her own talent. Writers are famously egotistical people, but they are also typically tormented by self-doubt. Ros’s supreme self-confidence was the reason for her producing such seductively mockable work, but it made her largely impervious to the mockery it provoked. She may have been a complete failure at the task she set for herself, but there was a certain greatness in her character.

Florence Foster Jenkins never considered herself on par with, say, Lily Pons, and, unlike Ros, she did much financially to support the art she loved. But that greatness was there. And if we couldn’t support her unironically in her lifetime, we can certainly — thanks to Stephen Frears, Nicholas Martin, Meryl Streep, and Hugh Grant — give her, on the occasion of Florence Foster Jenkins, a heartfelt “Brava!”